# In a certain district, the ratio of the number of registered republicans…

## Solution:

The fractional ratio indicates that for every 3 Republicans, there are 5 Democrats, a ratio of 3 : 5. We first set up this ratio of registered Republicans to registered Democrats using a variable multiplier:

Republicans: Democrats = 3x : 5x

We are given that 600 additional Republicans and 500 additional Democrats registered and that the new ratio of Republicans to Democrats was 4 to 5. This means that the new number of Republicans can be expressed as (3x + 600), and the new number of Democrats can be expressed as (5x + 500). We can put all this into an equation:

R/D –> (3x+600)/(5x+500) = 4/5

After cross multiplying we have:

5(3x+600) = 4(5x+500)

15x + 3,000 = 20x + 2,000

1,000 = 5x

x = 200

Thus after the registration we have the following:

Democrats = (5 × 200) + 500 = 1,500

Republicans = (3 × 200) + 600 = 1,200

There are 1,500 – 1,200 = 300 more Democrats than Republicans.

**Answer: B**